Problem: Solve for $y$, $ \dfrac{5}{25y + 25} = -\dfrac{2y - 7}{5y + 5} - \dfrac{1}{20y + 20} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $25y + 25$ $5y + 5$ and $20y + 20$ The common denominator is $100y + 100$ To get $100y + 100$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ \dfrac{5}{25y + 25} \times \dfrac{4}{4} = \dfrac{20}{100y + 100} $ To get $100y + 100$ in the denominator of the second term, multiply it by $\frac{20}{20}$ $ -\dfrac{2y - 7}{5y + 5} \times \dfrac{20}{20} = -\dfrac{40y - 140}{100y + 100} $ To get $100y + 100$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{1}{20y + 20} \times \dfrac{5}{5} = -\dfrac{5}{100y + 100} $ This give us: $ \dfrac{20}{100y + 100} = -\dfrac{40y - 140}{100y + 100} - \dfrac{5}{100y + 100} $ If we multiply both sides of the equation by $100y + 100$ , we get: $ 20 = -40y + 140 - 5$ $ 20 = -40y + 135$ $ -115 = -40y $ $ y = \dfrac{23}{8}$